scholarly journals New bounds for the Cebysev functional of two functions of selfadjoint operators in Hilbert spaces

Filomat ◽  
2010 ◽  
Vol 24 (2) ◽  
pp. 27-39 ◽  
Author(s):  
S.S. Dragomir
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Selfadjoint Operators ◽  
Čebyšev Functional ◽  
Subject Classifications ◽  
Mathematics Subject Classifications ◽  
New Inequalities

Some new inequalities for the Cebysev functional of two functions of selfadjoint linear operators in Hilbert spaces, under suitable assumptions for the involved functions and operators, are given. 2010 Mathematics Subject Classifications. 47A63; 47A99. .

scholarly journals Some inequalities for commutators of bounded linear operators in Hilbert spaces

Filomat ◽  
2011 ◽  
Vol 25 (2) ◽  
pp. 151-162 ◽  
Author(s):  
S.S. Dragomir
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
New Inequalities

Some new inequalities for commutators that complement and in some instances improve recent results obtained by F. Kittaneh are given.

scholarly journals Further Inequalities for Sequences and Power Series of Operators in Hilbert Spaces Via Hermitian Forms

2016 ◽  
Vol 2 (1) ◽  
pp. 47-64
Author(s):  
S. S. Dragomir
Keyword(s):  
Power Series ◽  
Hilbert Spaces ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Hermitian Forms ◽  
New Inequalities

Abstract By the use of some inequalities for nonnegative Hermitian forms some new inequalities for sequences and power series of bounded linear operators in complex Hilbert spaces are established. Applications for some fundamental functions of interest are also given.

Unbounded Linear Operators

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Von Neumann ◽  
Limit Circle ◽  
Sectorial Operators ◽  
Closed Operators ◽  
The Stability ◽  
Symmetric Operators ◽  
Unbounded Linear Operators ◽  
Special Case

This chapter is concerned with closable and closed operators in Hilbert spaces, especially with the special classes of symmetric, J-symmetric, accretive and sectorial operators. The Stone–von Neumann theory of extensions of symmetric operators is treated as a special case of results for compatible adjoint pairs of closed operators. Also discussed in detail is the stability of closedness and self-adjointness under perturbations. The abstract results are applied to operators defined by second-order differential expressions, and Sims’ generalization of the Weyl limit-point, limit-circle characterization for symmetric expressions to J-symmetric expressions is proved.

scholarly journals Sets of periods for chaotic linear operators

2021 ◽  
Vol 115 (2) ◽  
Author(s):  
J. A. Conejero ◽  
F. Martínez-Giménez ◽  
A. Peris ◽  
F. Rodenas
Keyword(s):  
Banach Spaces ◽  
Hilbert Spaces ◽  
Complete Characterization ◽  
Linear Operators

AbstractWe provide a complete characterization of the possible sets of periods for Devaney chaotic linear operators on Hilbert spaces. As a consequence, we also derive this characterization for linearizable maps on Banach spaces.

Elements of Spectral Theory for Generalized Derivations II : The Semifredholm Domain

1981 ◽  
Vol 33 (5) ◽  
pp. 1205-1231 ◽  
Author(s):  
Lawrence A. Fialkow
Keyword(s):  
Hilbert Spaces ◽  
Simple Formula ◽  
Decomposition Theorem ◽  
Linear Operators ◽  
Generalized Derivations ◽  
Bounded Linear ◽  
Infinite Dimensional ◽  
Hilbert Space Operators ◽  
Algebraic Invariants ◽  
Fredholm Theorem

Let and denote infinite dimensional Hilbert spaces and let denote the space of all bounded linear operators from to . For A in and B in , let τAB denote the operator on defined by τAB(X) = AX – XB. The purpose of this note is to characterize the semi-Fredholm domain of τAB (Corollary 3.16). Section 3 also contains formulas for ind(τAB – λ). These results depend in part on a decomposition theorem for Hilbert space operators corresponding to certain “singular points” of the semi-Fredholm domain (Theorem 2.2). Section 4 contains a particularly simple formula for ind(τAB – λ) (in terms of spectral and algebraic invariants of A and B) for the case when τAB – λ is Fredholm (Theorem 4.2). This result is used to prove that (τBA) = –ind(τAB) (Corollary 4.3). We also prove that when A and B are bi-quasi-triangular, then the semi-Fredholm domain of τAB contains no points corresponding to nonzero indices.

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